The Carnegie-Chicago Hubble Program: Calibration of the Near-Infrared RR Lyrae Period-Luminosity Relation With HST

Abstract: We present photometry of 30 Galactic RR Lyrae variables taken with HST WFC3/IR for the Carnegie-Chicago Hubble Program. These measurements form the base of the distance ladder measurements that comprise a pure Population II base to a measurement of Ho at an accuracy of 3%. These data are taken with the same instrument and filter (F160W) as our observations of RR Lyrae stars in external galaxies so as to to minimize sources of systematic error in our calibration of the extragalactic distance scale. We calculate mean magnitudes based on one to three measurements for each RR Lyrae star using star-by-star templates generated from densely time-sampled data at optical and mid-infrared wavelengths. We use four RR Lyrae stars from our sample with well-measured HST parallaxes to determine a zero point. This zero point will soon be improved with the large number of precise parallaxes to be provided by Gaia. We also provide preliminary calibration with the TGAS & Gaia DR2 data, and all three zero points are in agreement, to within their uncertainties.

• The paper establishes a robust calibration of the NIR RR Lyrae period-luminosity relation using HST F160W photometry.
• It employs template fitting for mean magnitude determination, mitigating phase sampling errors and aligning with Spitzer data.
• The approach minimizes systematic uncertainties in Population II distance measurements, supporting independent H0 determinations.

Calibration of the Near-Infrared RR Lyrae Period-Luminosity Relation with HST/WFC3 for the Carnegie-Chicago Hubble Program

Introduction

The paper presents a fundamental calibration of the near-infrared (NIR) period-luminosity (PL) relation for Galactic RR Lyrae (RRL) variable stars, using HST WFC3/IR F160W photometry. This work forms the base of the Population II distance ladder in the Carnegie-Chicago Hubble Program (CCHP), designed to provide a non-Cepheid, pure Population II calibration of the Hubble constant ($H_{0}$) with 3% accuracy. The authors emphasize the centrality of RR Lyrae-based PL relations at NIR wavelengths, due to reduced sensitivity to extinction and intrinsic scatter, for minimizing systematic errors in the extragalactic distance scale.

Observational Strategy and Data Acquisition

The sample includes 30 bright, well-studied Galactic RR Lyrae, with five stars already possessing high-precision ($\sim8\%$) HST/FGS trigonometric parallaxes and 25 others targeted for future Gaia parallaxes (anticipated precision $\sim1\%$). Observations were performed with the HST WFC3/IR in the F160W (H-band) filter to ensure equivalence with extragalactic RR Lyrae measurements. Due to extreme brightness, subarray and RAPID sampling modes, including drift-scan imaging, were employed to avoid detector saturation and mitigate non-linearity systematics. Photometric reduction was performed using DAOPHOT PSF photometry with careful masking of non-linear pixels and application of empirically determined aperture corrections tied to the HST flight magnitude system.

Mean Magnitude Determination

Given the sparsely-sampled NIR light curves, star-by-star template fitting was applied to determine intensity-averaged mean magnitudes. The methodology leverages well-sampled ground-based (BVI) and Spitzer (3.6 $\mu$m) light curves. The Spitzer GLOESS-smoothed light curves were shifted in magnitude to best match the HST data; the consistency between Spitzer- and template-derived mean magnitudes is notably high ($\langle\Delta m\rangle=0.005\pm0.019$ mag), validating the approach and mitigating concerns over phase sampling error. The F160W mean magnitudes are offset from 2MASS H-band values by $0.015\pm0.06$ mag, consistent with the expected systematic differences between the photometric systems.

Calibration of the Period-Luminosity Relation

Absolute magnitudes are computed using geometric parallaxes (HST/FGS, TGAS, Gaia DR2), incorporating extinction corrections. The core PL relation for F160W is adopted as:

$$M_{\lambda} = a_{\lambda} \times [\log P - 0.3] + b_{\lambda}$$

where fundamental mode (RRab) variables are selected, and the slope $a_{\lambda}$ is fixed to values from the literature and theoretical work. Both the direct parallax inversion and astrometry-based luminosity (ABL) approaches are applied to accommodate the varying quality of the parallax data.

Zero points ($b_{\lambda}$) are derived for each parallax sample, with/without accounting for metallicity dependence, and across both HST and ground-based H bands. The agreement among zero points from HST/FGS, TGAS, and Gaia DR2 is within their respective uncertainties (typical values $b_{\mathrm{F160W}}\sim -0.39\pm0.07$ mag using ABL for DR2), providing a robust calibration for subsequent rungs of the CCHP distance ladder.

Assessment of Systematics: Metallicity and Blazhko Effect

A PLZ relation, incorporating metallicity as:

$$M_{\lambda} = a_{\lambda} \times [\log P - 0.3] + b_{\lambda} + c_{\lambda}([\textrm{Fe/H}] + 1.60)$$

is evaluated, using $c_{\lambda}=0.186$ as the sensitivity of the zero point to metallicity. The resultant zero points exhibit consistency with the simple PL case, indicating that residual metallicity-dependent systematics are minor in the F160W calibration within present uncertainties. Stars displaying the Blazhko effect, known for amplitude and phase modulation, were analyzed for their impact; exclusion of Blazhko variables does not substantially alter the inferred zero point, particularly when using the ABL method.

Implications and Future Prospects

By establishing the NIR PL relation for RR Lyrae on the F160W HST system, this calibration enables Population II distance measurements in old, non-star-forming systems devoid of Cepheids—critically expanding the utility of the extragalactic distance ladder for $H_{0}$ determinations. The achieved internal consistency between various parallax-based calibrations demonstrates the resilience of the RR Lyrae PL relation to major systematic uncertainties at the current precision. However, the paper underlines that the forthcoming Gaia data releases, with large homogeneous samples of RR Lyrae parallaxes, will ultimately refine the zero point error to the requisite sub-0.03 mag (1.5%) level.

This approach, together with the TRGB and SNe Ia rungs, offers an independent validation of $H_{0}$ outside the canonical Population I (Cepheid-based) routes. By minimizing cross-instrumental and photometric systematics through an entirely HST-based path, this work sets a foundation for rigorously testing the current discrepancy (“Hubble tension”) between early and late Universe measurements.

Conclusion

This paper provides a methodologically robust and internally consistent calibration of the NIR RR Lyrae PL relation in the HST/WFC3 F160W band, directly supporting the Population II CCHP distance ladder. The strong agreement in zero point determinations across HST/FGS, TGAS, and Gaia DR2 parallax samples cements these RR Lyrae as high-precision primary distance indicators. The methodology and calibration strategy outlined here will facilitate significant reductions in systematic uncertainty in forthcoming measurements of $H_{0}$, especially as future Gaia data enable refinement to the RR Lyrae zero point. The present work is a pivotal step toward a Cepheid-independent Population II extragalactic distance scale based entirely on space-based NIR observations (1812.06053).